In this paper the KP-hierarchy signifies the following equation [1]} for the function
\(\tau (x)\)  of \(x={}^t(x_1,x_2,x_3,\dots )\) :
\(\oint {\rm e}^{-2\sum \limits _{j=1}^\infty y_j\lambda ^j}\tau \big (x-y-\big [\lambda ^{-1}\big ]\big )\tau \big (x+y+\big [\lambda ^{-1}\big ]\big )\frac{{\rm d}\lambda }{2\pi {\rm i}}=0,\) 
